Bach, 59, succeeds Jacques Rogge, whose 12-year tenure as IOC president ended Tuesday.
The IOC president is elected by IOC members for a term of eight years and is eligible for one four-year second term.
Bach was the leading vote-getter in the first round of voting Tuesday at the IOC meetings in Buenos Aires and collected a majority of the votes to win election in the second round.
Also on the ballot were Sergey Bubka from Ukraine, Richard Carrion from Puerto Rico, Ser Miang Ng from Singapore), Denis Oswald from Switzerland and Wu Ching-kuo Wu from Taipei. Carrion came in second in the voting.
"Thank you very much to all of you," Bach said following his election. "Let us, this great universal orchestra of IOC members, play together in harmony toward a bright future for the Olympic Movement under the leadership of the IOC."
Bach is chairman of the board of the Michael Weinig AG, a wood processing company with headquarters in Germany. He was on the German gold medal winning team in team foil at the 1976 Summer Games and in 1977 won the world championship in the foil competition.
He has been a member of the IOC since 1996 and has been an IOC vice president since 2006. He sought the IOC presidency under the slogan "Unity in Diversity."